duelSimulation [ p_, duelNum_ ] :=
Block[{duel,s,survivor},
s={0,0};
Do [survivor=duelOnce[p];
 s[[survivor]]=s[[survivor]]+1,{duel,1,duelNum}];
Do[s[[player]]=s[[player]]/duelNum,{player,1,Length[p]}];
s
]

duelOnce [ p_ ] :=
Block[{r,survivor,turnNum},
turnNum = 0;
While [True,
turnNum = turnNum + 1;
r = Random[];
If[r < p[[1]],survivor = 1; Break[]];
turnNum = turnNum + 1;
r = Random[];
If[r<p[[2]], survivor = 2; Break[]]
];
survivor
]

p={3/6,2/6};
N[duelSimulation[p,100]]